This invention relates in general to monitoring, analyzing and modifying the pulsating behavior of active systems, and in particular that of living cardiac tissue.
The realization that many activities of an apparently random nature are actually examples of a deterministic phenomenon known as chaos offers a new approach to analysis and modification of complex systems. Phenomena that have been shown to exhibit chaos include the transition to turbulence in fluids, many mechanical vibrations, irregular oscillations in chemical reactions, the rise and fall of epidemics and the irregular dripping of a faucet. Several studies have argued that certain cardiac arrhythmias are also examples of an irregular pulsating behavior characterizable as chaos.
Until recently the main strategy for dealing with a system exhibiting chaos was to develop a model of the system sufficiently detailed to identify the key parameters and then to change those parameters enough to take the system out of the chaotic regime. However that strategy is limited to systems for which a theoretical model is known and which do not display irreversible parametric changes (often the very changes causing the chaos) such as aging. Recently, a strategy was developed which does not attempt to take the system out of the chaotic regime but uses the chaos to control the system. The critical feature of chaos believed to make this possible is the extreme sensitivity of chaotic systems to perturbations of their initial conditions. The key to such strategy lies in the fact that chaotic motion includes an infinite number of unstable periodic motions. A chaotic system never remains long in any of such unstable motions but continually switches from one periodic motion to another, thereby giving the appearance of randomness. It was conjectured that it should be possible to stabilize a chaotic system around selected periodic motions. Such system stabilizing theory and approach was first applied experimentally (a) to controlling the chaotic vibrations of a magnetoelastic ribbon and (b) subsequently applied to a diode resonator circuit and (c) in the chaotic output of lasers. Such chaos controlling strategy involved development of a real-time measurement of the current system state and identification of an unstable fixed point of interest on a plot along with its stable and unstable manifolds. Such fixed point and its accompanying manifolds shift in response to changes in system-wide parameters. Thus, a feedback providing algorithm was developed tending to move the fixed point and manifolds toward the system state point on the aforementioned plot in response to corrective control of the selected system-wide parameter. Unfortunately, a system-wide parameter capable of being changed with sufficient rapidity to implement corrective control in accordance with the foregoing strategy was not found to be suitable in certain cases for stabilization purposes.
It is therefore an important object of the present invention to provide a method and apparatus for manipulating chaotic behavior based on the aforementioned study of chaotic regimes by intervention at irregular times determined from real time calculations involving data obtained by monitoring a selected observable system behavior.